Collective variables between large-scale states in turbulent convection

The dynamics in a confined turbulent convection flow is dominated by multiple long-lived macroscopic circulation states that are visited subsequently the system Markov-type hopping process. In present work, we analyze short transition paths between these subsequent data-driven learning algorithm extracts low-dimensional manifold and related new coordinates, which term collective variables, state space of complex flow. We therefore transfer extend concepts for conformation transitions stochastic microscopic systems, such as macromolecules, to deterministic Our analysis based on long-term direct numerical simulation trajectories closed cubic cell at Prandtl number $\text{Pr}=0.7$ Rayleigh numbers $\text{Ra}={10}^{6}$ ${10}^{7}$ time lag ${10}^{5}$ convective free-fall units. simulations resolve vortices plumes all physically relevant scales, resulting spanned more than 3.5 million degrees freedom. large-scale can be captured with only two implies reduction data dimension factor million. method demonstrates cessations reversals unlikely setup, thus it paves way development efficient reduced-order models nonlinear dynamical system.